Understanding fractions (age 10+)

Question 1

Jamie wants to make 3 batches of pancake mix. Each batch uses 2/5 cup of milk. Which choice correctly shows the algebraic equation for the total milk needed and a correct description of a bar model that represents the situation?

Accepted Answer

Equation: total = 3 × (2/5) = 6/5 cups. Bar model: three identical bars, each divided into 5 equal parts with 2 parts shaded; together the shaded parts make 6 of the 5 parts (one whole bar plus one extra part).

Answer

Equation: total = 3 + (2/5) = 17/5 cups. Bar model: three whole bars and, on a fourth bar, 2 of the 5 parts are shaded.

Answer

Equation: total = (2/5) ÷ 3 = 2/15 cups. Bar model: one bar divided into 5 parts, 2 parts shaded, then the whole bar is split into 3 equal sections.

Answer

Equation: total = 3 × (5/2) = 15/2 cups. Bar model: three bars, each divided into 2 parts with 5 parts shaded on each bar.

Question 2

Lila is preparing lemonade for a school event. She needs to fill 4 identical jars, and each jar requires 3/8 liter of lemon juice. Which option shows the correct algebraic equation for the total amount of lemon juice needed and correctly describes a bar model that represents this situation?

Accepted Answer

Equation: 4 × 3/8 = total lemon juice. Bar model: Four separate bars, each divided into 8 equal parts with 3 parts shaded; the shaded parts from all four bars together show the total.

Answer

Equation: 4 + 3/8 = total lemon juice. Bar model: One whole bar representing 4 liters plus a small bar divided into 8 parts with 3 shaded.

Answer

Equation: 4 × 3/8 = 12/8 liters. Bar model: A single bar divided into 8 equal parts with 12 parts shaded.

Answer

Equation: 3/8 × 4 = 3/2 liters. Bar model: Three bars, each divided into 8 parts with 4 parts shaded.

Question 3

In a class of 20 students, 5 students like chocolate ice cream. The teacher draws a pie chart and shades the part that represents the students who like chocolate. Which statement correctly shows the fraction, the percentage, and the portion of the pie chart that all represent the same proportion?

Accepted Answer

5/20, which simplifies to 1/4; this is 25% of the circle, so the shaded part is one quarter of the pie chart.

Answer

5/20, which simplifies to 1/5; this is 20% of the circle, so the shaded part is one fifth of the pie chart.

Answer

5/20, which simplifies to 1/4; this is 30% of the circle, so the shaded part is about one third of the pie chart.

Answer

5/20, which simplifies to 1/2; this is 50% of the circle, so the shaded part is half of the pie chart.

Try three questions

Jamie wants to make 3 batches of pancake mix. Each batch uses 2/5 cup of milk. Which choice correctly shows the algebraic equation for the total milk needed and a correct description of a bar model that represents the situation?

Lila is preparing lemonade for a school event. She needs to fill 4 identical jars, and each jar requires 3/8 liter of lemon juice. Which option shows the correct algebraic equation for the total amount of lemon juice needed and correctly describes a bar model that represents this situation?

In a class of 20 students, 5 students like chocolate ice cream. The teacher draws a pie chart and shades the part that represents the students who like chocolate. Which statement correctly shows the fraction, the percentage, and the portion of the pie chart that all represent the same proportion?

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